Mathematical Models for Economic and Political Advertising Campaigns

We propose a basic model for a two-competitor advertising campaign. Game-theoretic saddle-point solutions are found for the following four problems. How large should the total advertising budget be to maximize profits? How should the budget be distributed in a differentiated market, and how much is saved by this distribution? How should one distribute advertising dollars in order to maximize one's expected total number of votes on a political campaign? How should one allocate expenditures over time in order to maximize one's expected number of votes at election day? Finally, the model is tested against empirical data from actual election campaigns and is found to yield a very high correlation between actual and predicted behavior.